ECON1003 Quantitative Methods in Economics
The Complete Exam Bible · S1 2026ECON1003 Overview
- University of Sydney
- S1 2026
- 7 chapters
- Economics
Quantitative Methods in Economics is the maths engine room of an economics degree — and despite the name it is mathematics, not statistics (no mean, no probability, no regression).
- Assessed by Final examination 50% · Mid-semester exam 40% · Online quizzes 10%
- Key terms Slope-intercept form, Elasticity (point form), Present value (NPV), Lagrangian
- How to prepare Every ECON1003 exam question is procedural: take a function or a system, apply the right technique, interpret the economics, round as asked.
- Most asked What's the best way to study for the ECON1003 exams?
How ECON1003 is assessed
| Component | Weight | Format |
|---|---|---|
| Final examination | 50% | End-of-semester exam · cumulative across all seven topics · formula sheet provided |
| Mid-semester exam | 40% | 60 minutes · covers the early topics (lines, non-linear functions, financial maths and the start of differentiation) · formula sheet provided |
| Online quizzes | 10% | Four quizzes on Canvas across the semester, one week each — confirm the exact split and dates in your unit guide |
What ECON1003 covers
Seven taught topics → one exam-ready map. Each links to its free chapter guide.
Linear Functions
y = mx + c · demand & supply · cost/revenue · linear elasticity02Non-Linear Functions
Quadratics & the discriminant · exponentials & e · logs · growth03Financial Mathematics
Series · simple/compound/continuous interest · NPV · annuities04Differentiation
The rules · optimisation · turning points · MR = MC profit max05Multivariable Calculus
Partials · total differential · MRS/MRTS · the Lagrangian06Integration
Anti-derivatives · area & surplus · recovering TC from MC · ODEs07Linear Algebra
Matrices · determinants · Cramer's rule · the inverse · solving systemsIt teaches seven techniques, all drilled on economic examples: straight lines, non-linear functions, financial mathematics, differentiation, functions of several variables, integration and linear algebra. A formula sheet is provided in both exams, so the examiner cannot test whether you remember a formula — only whether you can apply it.
This guide teaches every method to exam standard: the rule stated plainly, the worked example with real arithmetic, and where the marks hide.
Profit maximisation by differentiation — the signature MR = MC question, mark by mark
- +1Write revenue and profit. TR = P×Q = (100 − 2Q)Q = 100Q − 2Q². Profit π = TR − TC = (100Q − 2Q²) − (20Q + 50) = 80Q − 2Q² − 50.
- +1Differentiate and set to zero (the first-order condition). dπ/dQ = 80 − 4Q = 0.
- +1Solve for Q*. 4Q = 80 ⇒ Q* = 20. (Equivalently MR = 100 − 4Q equals MC = 20 at the same Q.)
- +1Find the price from inverse demand: P* = 100 − 2(20) = $60.
- +1Confirm it is a maximum (second-order condition). d²π/dQ² = −4 < 0, so the profit function is concave — Q* = 20 is a maximum, not a minimum.
- +1State the result. Maximum profit π = 80(20) − 2(20)² − 50 = 1600 − 800 − 50 = $750.
Key terms
- Slope-intercept form
- Any straight line written y = mx + c, where m is the slope (how much y changes when x rises by one) and c is the y-intercept (y when x = 0). The workhorse of every linear model in the unit — demand, supply, cost, a budget line.
- Elasticity (point form)
- The responsiveness of quantity to price as a unit-free number, ε = (dQ/dP)(P/Q). The key trap the unit exploits: on a straight-line demand the slope dQ/dP is constant but elasticity changes along the curve, because P/Q changes — so elasticity is not the slope.
- Present value (NPV)
- Today's worth of a future cash flow, found by discounting it back at the interest rate. Net present value sums the discounted inflows minus the cost; a positive NPV means the project adds value. It is the financial-maths topic's payoff calculation.
- Lagrangian
- The technique for constrained optimisation — maximise utility or minimise cost subject to a budget or output constraint. You form L = objective + λ(constraint), set the partial derivatives to zero, and solve; λ is the shadow price, the marginal value of relaxing the constraint. The unit's flagship, highest-mark technique.
- Determinant
- A single number computed from a square matrix that tells you whether the matrix is invertible (det ≠ 0) and underpins Cramer's rule for solving systems. The 2×2 is ad − bc; the 3×3 expands along a row with the + − + sign pattern.
ECON1003 FAQ
Is ECON1003 statistics?
No — and this is the single most common misconception. Despite the name 'Quantitative Methods', ECON1003 is mathematics for economics, not statistics. There is no mean, no probability, no hypothesis testing and no regression.
The seven taught topics are straight lines, non-linear functions, financial maths, differentiation, multivariable calculus, integration and linear algebra — calculus and algebra dressed in demand, cost, utility and production.
How is ECON1003 assessed?
By two written exams and online quizzes: a mid-semester exam (about 40%, 60 minutes, covering the early algebra-and-functions material plus the start of differentiation), a cumulative final exam (about 50%, all seven topics), and four online Canvas quizzes (about 10%, one week each). A formula sheet is provided in both exams. Confirm this year's exact weights and dates in your unit guide.
Do I need to memorise all the formulas?
No — a formula sheet is provided in both exams, so the examiner is testing method, not recall. The sheet typically carries the quadratic formula, the interest/annuity/NPV formulas, integration by parts and the aˣ/log derivatives.
What you must wield cold are the procedures: the differentiation rules (power, sum, product, quotient, chain), how to set up TR = P×Q, the Lagrangian conditions, and the matrix methods (elimination, Cramer, inverse).
What's the best way to study for the ECON1003 exams?
Drill the recurring procedural chains until they are automatic, because every exam question is procedural: line → slope/intercept → elasticity; set up TR → differentiate → MR = MC; integrate MC → recover TC; Lagrangian → solve cases → shadow price. Always show every line — method marks and partial credit are real even when the final arithmetic slips.
Is using AskSia for ECON1003 cheating?
No. AskSia is a study reference written in our own words — we host none of your lecturer's files, and Sia teaches you the method to earn the marks; it does not complete or sit your assessments.
How to study for the exam
Every ECON1003 exam question is procedural: take a function or a system, apply the right technique, interpret the economics, round as asked. So the win condition is fluent, automatic technique — not memorised formulas (the sheet hands you those).
Drill the recurring chains until they are reflex: line → slope/intercept → elasticity; set up TR = P×Q → differentiate → MR = MC; integrate MC → recover TC; Lagrangian → solve cases → shadow price. Always show every line — method marks and partial credit are real.
Weight your time toward differentiation and the multivariable Lagrangian (they carry the most marks and span both exams), and treat financial maths as free procedural marks once you pick the right formula. Practise on fresh numbers so nothing in the exam can surprise you.
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